Quite a few organisations (both profit and non-profit organisation) cary more than one brand. General Motors became famous for it, thanks to Alfred Sloan, who developed the multi-brand approach on a huge scale.
An organisation to have various faces to the out-side world enables it to interact better with its audiences, because it allows various connections with various people in suited ways.
On the other hand it requires a delicate internal organisation to match the need and benefits of one-ness with the advantages of differentiation and autonomy. The worst outcome would be organisational schizophrenia, a not so un-common managerial disease.